Question

Factor completely.

Y^2-12y+32

A. (y+4)(y+8)
B. (y-4)(y-8)
C. (y+18)(y + 2)
D. (y-18)(y-2)

Answer 1

B. (y-4)(y-8)

Explanation:

Given equation: y² - 12y + 32. Essentially, we are going to find two numbers that multiply to 32 and add up to -12.

1) Pull out the factors of 32 and find the pair that multiply to 32 and add up -12.

They are: -8 and -4.

2) Rewrite the b of the original quadratic equation as a sum, then factorise by grouping.

y² - 8y - 4y +32

y(y - 8) - 4(y - 8)

(y - 4)(y -8)

Answer 2

B

Explanation:

y² - 12y + 32

consider the product of factors of the constant term (+ 32) which sum to give the coefficient of the y- term (- 12)

the factors are - 4 and - 8 , since

- 4 × - 8 = + 32 and - 4 - 8 = - 12 , then

y² - 12y + 32 = (y - 4)(y - 8)